# physics

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A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s.
How can I derive the equation for the trajectory of the probe during the time the rocket is fired using the formula y = a function of x and compute the final speed of the rocket at the end of the 1.5 s?

• physics -

Thrust is in force units. For all intents and purposes, there is a force in the y-direction of 1800 N for 1.5 seconds.

The motions in the x- and y-directions being linearly independent, we can process them separately and relate the motion using the parameter t=time.

vx(t)=12 m/s (constant)
force in y-direction, F = 1800 N
mass, m = 2000 kg
Since Force F=ma, where a = acceleration
acceleration=F/m=1800/2000 m/s²
=0.9 m/s²
Initial velocity in the y-direction = 0
therefore
vy(t)=0+at=0.9t (0≤t≤1.5)

The trajectory is given by the parametric formulae vx(t) and vy(t) in terms of time, t.

The speed at any time t within the firing period (1.5 s) can be obtained by the vectorial sum of the two velocities, vx(t) and vy(t):

Speed for 0≤t≤1.5
S(t)=sqrt(vx(t)²+vy(t)²)
=sqrt(12²+(0.9t)²)

Speed at the end of the rocket firing period
=S(1.5)

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